A few discoveries in the vicinity of B01345/S234:
• A domino in B0134567/S2345 turns out to be a "chaotic replicator"; it's neither a 2ⁿ sawtooth nor a self-standing wickstretcher. It does have a definite period and speed, however (4c/8 namely). I am not sure if gaps appearing in the replicator stream have an upper size limit or not.
In 4-divisible generations, the pattern settles down to rectangles of width 2 and odd length. The maximum size of these rectangles seems to grow over time, and as a rectangle's center leaves a blank space, this seems like an easy metric to track:
—g0: 1 (= domino)
—g4: 5
—g20: 7
—g28: 9
—g40: 13
—g64: 19
—g220: 21
—g244: 49
Moreover, it is not even trivial to see that this pattern even remains a replicator indefinitely, as a rectangle of 2×4, were one to occur, will explode…
• I reported in the alternating rules topic a rule which explodes only along even mirror axes. I seem to have found a plain example of the same: B013458/S02345. For instance:
Code: Select all
x = 348, y = 2, rule = B013458/S02345
o10bo333bobo$o10bo!
Overall this is a stabilizing rule. Those ubiquitous p2 "pods" grow from a single domino; any number of other more or less rectangular p2s are possible. Note also the butterfly-like p18 and the two p4s you can see in the ash of the methuselah above.
There's also a c/10 ladder and c/10 and c/6 wicks:
Code: Select all
x = 32, y = 25, rule = B013458/S02345
31bo$b28o$bo$b28o$31bo4$21bo$b20o$b20o$b20o$b20o$21bo4$b5o$b5o$b5o$6o$
6o$b5o$b5o$b5o!
• Speaking of ladders, I find B013456/S234 a fairly interesting rule. It is chaotically exploding, but in an unusual fashion — it leaves perfectly still sparse ash behind, much like your usual stabilizing rule. All growth seems to occur due to the ubiquitous c/4 "shoots"; if perturbed, they burn cleanly at c/2 (at period 48). Once this reaches the end, a number of things may happen to the shoot:
—dies out cleanly
—leaves some debris
—gives birth to one sideways shoot (plus a little debris?)
—gives birth to two sideways shoots
—is cleanly reborn and continues in both directions
—the back end stabilizes, the front end continues
—gives birth to a backwards shoot stabilized from the front
Also, a shoot's end hitting the stalk of another will, in addition to igniting the second one in both directions, create two new shoots alongside the first one.
I find this rule very interestign to watch. This is the smallest chaotic growth pattern I've found:
Code: Select all
x = 14, y = 3, rule = B013456/S234
2o9b3o$2o9b3o$2o!
And here's a collection of other ladder shapes, with wider ones at c/8, c/16, and c/76, and a c/12 fuse for the basic shoot:
Code: Select all
x = 54, y = 22, rule = B013456/S234
48b2o$48b2o$48b2o8$2o7b2o9b2o3b2o6b5o$2o7b2o7b11o4b2ob4o4b10o$3o6b2o7b
11o4b7o4b10o$9b2o7b11o4b7o4b10o$18b11o4b7o4b10o2$7b6o$7b6o$7b6o$7b6o$
8b4o$9b2o!